Analyzing the performance of queueing networks that do not admit a product form solution is a challenging problem. In this thesis we present some tools for doing so. Our attention is restricted to Markovian queueing networks.We first present a technique for bounding the performance of such networks. Assuming a steady state for functionals of the state, we obtain linear programs which bound the performance. This technique is illustrated using quadratic functionals to bound the performance of a class of Markovian queueing networks called reentrant lines. We also show how this technique may be applied to bound throughput and blocking probabilities in networks with buffer capacity constraints. In some cases bounds obtained using multimedial functional of the state are shown to approach the exact value when the degree of the multimedial increases.We also study another important technique for the analysis of queueing networks, namely, the fluid limit approach. This approach is used to establish the stability of a class of policies called Fluctuation Smoothing policies for open reentrant lines. We also show how the fluid limit approach can be used to obtain the asymptotic performance of closed queueing networks in heavy traffic. We then use fluid limits to establish the efficiency of Fluctuation Smoothing policies for closed reentrant lines, as well as the Harrison-Wein policy for two station closed reentrant lines.